We analyze the dynamic behavior of Newtonian fluids in elastic tubes subject to pulsatile pressure gradients and show that the interplay between the viscosity of the fluid, the elasticity of the wall, and the characteristic size of the confining media gives rise to a rich phenomenology that includes resonances. We find that these resonances are relevant for small confining geometries with low Young's moduli, typical of elastomeric materials in microfluidics. These resonances disappear beyond a certain tube radius, a certain Young's modulus, and below a certain fluid viscosity. In order to guide potential experiments, we present results for mineral oil flowing through polydimethylsiloxane microtubes and find resonances of the order of few tens of kHz. Published by AIP Publishing.